1. Field of the Invention
The present invention relates to a method of producing an inverse discrete cosine transform (IDCT), and more particularly to a method of producing an IDCT capable of reducing the amount of calculation while satisfying the bit accuracy required by international standards.
2. Description of the Prior Art
The discrete cosine transform (DCT) has been widely used as a data compression technique using correlation among pixels of an image. The technique has been adopted for international standards such as MPEG, JPEG, H.261, etc. Accordingly, in a receiving apparatus for receiving image data which is compressed using DCT, the IDCT is required to recover information which was compressed using this technique. Since DCT requires a large amount of multiplication, addition and subtraction, research for high-speed calculation is now in progress.
Various techniques have been utilized to reduce the amount of calculation or time required to perform the IDCT. One technique is taught by J. Yang, "An Efficient Two-Dimensional Inverse Discrete Cosine Transform Algorithm for HDTV Receivers", IEEE Trans. Circuits and Systems for Video Technology, Vol. 5, No. 1, February, 1995. However, the arithmetic operations disclosed by Yang cannot be easily vectorized. As a result, the parallel processing of the operations is difficult, and the amount of calculation is increased.
Another technique is taught by N. Demassieux and F. Jutand, "Orthogonal Transforms in VLSI Implementations for Image Communications", edited by P. Pirsch, Elsevier Science Publisher, The Netherlands, 1993. The Butterfly chain based fast algorithm disclosed by Demassieux and Jutand includes numerous multiplication operations which deteriorate bit accuracy and cause non-compliance with the international standards previously mentioned.
Typically, the IDCT is performed using a floating-point processor because of the cosine values used in the IDCT. In order to achieve high-speed processing, a high-performance processor is required, thereby increasing the cost of the receiving apparatus.
A two-dimensional IDCT is given by
Mathematical Expression 1 ##EQU3## If we define ##EQU4## the mathematical expression 1 can be expressed as the matrix expression which is given by
Mathematical Expression 2
[f]=[c][F][C].sup.T
Here, the transposed matrix C.sup.T corresponds to a one-dimensional IDCT in a vertical direction, and the matrix C corresponds to a one-dimensional IDCT in a horizontal direction. Accordingly, in order to calculate a two-dimensional IDCT, calculation processes in both horizontal and vertical directions should be performed. A general vector processor can perform a parallel process only in one direction. Therefore, the vectorization of the operations in both directions cannot be achieved.